Strongly Nonlocal Dislocation Dynamics in Crystals
Strongly Nonlocal Dislocation Dynamics in Crystals
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DOI：
10.1080/03605302.2014.914536
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发表时间：
2013-11
影响因子：
1.9
通讯作者：
S. Dipierro;A. Figalli;E. Valdinoci
中科院分区：
文献类型：
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作者：
S. Dipierro;A. Figalli;E. Valdinoci
本文考虑如下方程，其中Ls是2s阶积分微分算子，s ∈（0，1），W是周期势，σ_n是小的外应力.解v表示Peierls-Nabarro晶体模型中的原子位错，我们特别考虑了s ∈（0，1/2）的情况，其中考虑了强非局部弹性项。我们研究了宏观时空尺度下位错函数的演化，即引入了位错函数，并证明了在小尺度下位错函数v_∞逼近阶跃函数之和。从物理的角度来看，这表明位错有集中在晶体的单点的趋势，在那里滑移的大小与介质的自然周期性一致。我们还表明，这些位错点的运动是由一个内部的排斥潜力，是叠加到一个弹性反应的外部应力。
We consider the equation where L s is an integro-differential operator of order 2s, with s ∈ (0, 1), W is a periodic potential, and σϵ is a small external stress. The solution v represents the atomic dislocation in the Peierls–Nabarro model for crystals, and we specifically consider the case s ∈ (0, 1/2), which takes into account a strongly nonlocal elastic term. We study the evolution of such dislocation function for macroscopic space and time scales, namely we introduce the function We show that, for small ϵ, the function v ϵ approaches the sum of step functions. From the physical point of view, this shows that the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. We also show that the motion of these dislocation points is governed by an interior repulsive potential that is superposed to an elastic reaction to the external stress.